Question

what are the roots of the following function? f(x) (4x-1)(x+9)
please answer due today.
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Answer 1

Answer:

$x=-9, \quad x=\dfrac{1}{4}$

Step-by-step explanation:

Given function:

$f(x)=(4x-1)(x+9)$

The roots of a function are the x-values for which the function equals zero.  Therefore, to find the roots, set the function to zero and solve for x.

Set the function to zero:

$\implies f(x)=0$

$\implies (4x-1)(x+9)=0$

Zero Product Property

If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Apply the zero product property:

$(4x-1)=0 \implies x=\dfrac{1}{4}$

$(x+9)=0 \implies x=-9$

Therefore, the roots of the given function are:

$x=-9, \quad x=\dfrac{1}{4}$